**is the point where the graph intersects the**

*x*-intercept*x*-axis and the

**is the point where the graph intersects the**

*y*-intercept*y*-axis. These points have the form (

*x*, 0) and (0,

*y*) respectively.

To find the

*x*- and

*y*-intercepts algebraically, we use the fact that all

*x*-intercepts have a

*y*-value of zero and all

*y*-intercepts have an

*x*-value of zero. For example,

**Graph:**3

*x*− 5

*y*= 15

**Tip 1:**To find the

*y*-intercept, set

*x*= 0 and determine the corresponding

*y*-value. Similarly, to find the

*x*-intercept we set

*y*= 0 and determine the corresponding

*x*-value.

Keep in mind that the intercepts are ordered pairs and not numbers. In other words, the

*x*-intercept is not

*x*= 5 but rather (5, 0).

Two points determine a line. If we find the

*x*- and

*y*-intercepts, then we can use them to graph the line. As you can see, they are fairly easy to find. Plot the points and draw a line through them with a straightedge.

Done. Let’s do another one.

**Graph:**

*y*= −

*x*+ 9

*x*-intercept.

The

*x*-intercept is (3, 0).

The

*y*-intercept is (0, 9). Now graph the two points.

**Tip 2:**Use Desmos.com to check your answer – it’s totally free. Just type in the equation.

This is a nice and easy method for determining the two points you need for graphing a line. In fact, we will use this exact technique for finding intercepts when we study the graphs of all the conic sections later in our study of Algebra.

**Graph**−4

*x*+ 3

*y*= 12 using the intercepts.

**Graph**−4

*x*+ 2

*y*= −6 using the intercepts.

**Graph**

*y*= −5x +15 using the intercepts.

**Graph**

*y*= −3/4

*x*+ 9 using the intercepts.

This brings us to one of the most popular questions in linear graphing. Do all lines have

*x*- and

*y*-intercepts? The answer is NO. Horizontal lines, of the form

*y*=

*b*, do not necessarily have

*x*-intercepts. Vertical lines, of the form

*x*=

*a*, do not necessarily have

*y*-intercepts.

**Graph**

*y*= 3.

**Graph**

*x*= −2.

Many students this method, but I will tell you, there is a better way. Even less work... [ Graph Lines using Slope and Intercepts ] Read on!

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